Optimal material properties for transient problems

The aim of this article is to analyze the problem of optimizing material properties within the context of a time-dependent problem. The objective is to minimize the difference between the actual values of a field variable and a desired “target” distribution after a prescribed time T. The field variable is related to a transient physical phenomenon with given initial and boundary conditions. The time-independent material properties are taken as the design variables. For simplicity, only the case of transient heat conduction is analyzed, though the method can be naturally extended to elastodynamics. Examples and test cases are solved numerically for different types of boundary conditions and target functions using a scaled-gradient method. The scaling function serves the purpose of satisfying constraints, but can also be used as an implicit penalty formulation to obtain optimal topologies by introducing an additional bias in the scaling. Its performance is compared to the unbiased method. Received July 25, 2000     

A hierarchical computational model for moving thermal loads and phase changes with applications to selective laser melting

Computational heat transfer analysis often involves moving fluxes which induce traveling fronts of phase change coupled to one or more field variables. Examples are the transient simulation of melting, welding or of additive manufacturing processes, where material changes its state and the controlling fields are temperature and structural deformation. One of the challenges for a numerical computation of these processes is their multi-scale nature with a highly localized zone of phase transition which may travel over a large domain of a body. Here, a transient local adaptation of the approximation, with not only a refinement at the phase front, but also a de-refinement in regions, where the front has passed is of advantage because the de-refinement can assure a bounded number of degrees of freedom which is independent from the traveling length of the front.We present a computational model of this process which involves three novelties: (a) a very low number of degrees of freedom which yet yields a comparatively high accuracy. The number of degrees of freedom is, additionally, kept practically constant throughout the duration of the simulation. This is achieved by means of the multi-level $hp$-finite element method. Its exponential convergence is verified for the first time against a semi-analytic, three-dimensional transient linear thermal benchmark with a traveling source term which models a laser beam. ( b) A hierarchical treatment of the state variables. To this end, the state of the material is managed on a separate, octree-like grid. This material grid may refine or coarsen independently of the discretization used for the temperature field. This methodology is verified against an analytic benchmark of a melting bar computed in three dimensions in which phase changes of the material occur on a rapidly advancing front. (c) The combination of these technologies to demonstrate its potential for the computational modeling of selective laser melting processes. To this end, the computational methodology is extended by the finite cell method which allows for accurate simulations in an embedded domain setting. This opens the new modeling possibility that neither a scan vector nor a layer of material needs to conform to the discretization of the finite element mesh but can form only a fraction within the discretization of the field- and state variables.     

Obtaining a hyperelastic non-linear orthotropic material model via inverse bubble inflation analysis

An inverse bubble inflation test is proposed utilizing full displacement field matching to obtain non-linear material models suitable for the Finite Element (FE) method. In this paper a known non-linear orthotropic material model is assumed as the solution for the inverse method to illustrate the process. A bubble inflation FE analysis is performed with the known material model to determine the load and displacement field from the assumed material. Polynomial surfaces are fit to the nodal displacement values of the FE model, such that the entire displacement field is stored as three unique polynomial surfaces. An error formulation was established to quantify the quality of fit between different bubble inflation displacement fields. Gradient based optimization is used to obtain the assumed material model by matching the full displacement field. The inverse bubble inflation test successful produces a non-linear orthotropic model that is analogous to the assumed non-linear orthotropic material, and thus demonstrates that the inverse bubble inflation analysis would be able to characterize other non-linear orthotropic materials.     

Evaluation of thermal energy storage and recovery for an electrical energy mediator system

Energy storage both electrical and thermal is a rapidly emerging field of interest toward the development of more sustainable energy systems. The inherent inefficiencies associate with electrical storage can be partially overcome when thermal storage that collects and storage the waste thermal energy for alternative uses is integrated. Consequently, thermal energy storage systems are an enabling technology that will allow increased energy efficiency of a community, permit load levelling to reduce peak electricity demand. In order to facilitate a technology evaluation, a sizing strategy is developed for a phase change material (PCM) thermal storage system that determines system requirements under given thermal energy capture and recovery cycles. The sizing process utilizes a simplified one-dimensional heat transfer model that estimates melt times for a phase change material thickness without detailed geometry information. This melt time estimate allows the proportion of phase change material to fluid routing materials to be calculated, giving an estimate of material cost for the thermal storage cell to determine economic feasibility. The model is compared to both experimental data and computational fluid dynamics models in order to determine its limitations. Through a specific example of hydrogen based distributed electrical energy mediator system, the utility of the sizing model in determining the estimated cost of thermal energy storage is demonstrated.     

Automated time domain modeling of linear and nonlinear microwave circuits using recurrent neural networks

In this article, a recurrent neural network (RNN) method is employed for dynamic time‐domain modeling of both linear and nonlinear microwave circuits. An automated RNN modeling technique is proposed to efficiently determine the training waveform distribution and internal RNN structure during the offline training process. This technique extends a recent automatic model generation (AMG) algorithm from frequency‐domain model generation to dynamic time‐domain model generation. Two types of applications of the algorithm are presented, transient electromagnetic (EM) behavior modeling of microwave structures, and time‐domain envelope modeling of power amplifiers (PA). For transient EM modeling, we consider EM structures with varying material and geometrical parameters. AMG automatically varies the EM structural parameters during training and drives time‐domain EM simulators to generate necessary amount of data for RNN to learn. AMG aims to model the transient behavior with minimum RNN order while satisfying accuracy requirements. In modeling PA behavior, an envelope formulation is used to specifically learn the AM/AM and AM/PM distortions due to third‐generation (3G) digital modulation input. The RNN PA model is able to model these time domain distortions after training and can accurately model the amplifier behavior in both time (AM/AM, AM/PM) and frequency (spectral re‐growth). © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2008.     

Thermal and flow analysis of a magneto-hydrodynamic micropump

A study of transient fully developed laminar flow and temperature distribution in a magnetohydrodynamic (MHD) micropump is presented. The micropump is driven using the Lorentz force which is induced as a result of interaction between an applied electric field and a perpendicular magnetic field. The governing equations are solved analytically by an eigenfunction expansion method, and numerically by a finite-difference (ADI) method. The numerical and analytical results are found to be in good agreement with each other. The effect of different parameters on the transient velocity and temperature, such as aspect ratio, Hartman number, Prandtl number, and Eckert number is studied. The results obtained showed that controlling the flow and the temperature can be achieved by controlling the potential difference, the magnetic flux, and by a good choice of the electrical conductivity.     

Microwave nondestructive evaluation of dielectric materials with a metamaterial lens

A novel microwave nondestructive evaluation (NDE) sensor was developed in an attempt to increase the sensitivity of the microwave NDE method for detection of defects small relative to a wavelength. The sensor was designed on the basis of a negative index material (NIM) lens. Characterization of the lens was performed to determine its resonant frequency, index of refraction, focus spot size, and optimal focusing length (for proper sample location). A sub-wavelength spot size (3 dB) of 0.48λ was obtained. The proof of concept for the sensor was achieved when a fiberglass sample with a 3 mm diameter through hole (perpendicular to the propagation direction of the wave) was tested. The hole was successfully detected with an 8.2 cm wavelength electromagnetic wave. This method is able to detect a defect that is 0.037λ. This method has certain advantages over other far field and near field microwave NDE methods currently in use.     

Transient detection with an application to a chemical process

We propose a sequential test procedure for transient detections in a stochastic process which can be expressed as an autoregressive moving average (ARMA) model. Preliminary analysis shows that if an ARMA(p,q) time series exhibits a transient behavior, then its residuals behave as an ARMA(Q,Q) process, where Q ≤ p + q. Based on this fact, we derive a new sequential test to determine when a transient behavior occurs in a given ARMA time series. Simulation experiments conducted in this study show that the proposed test can detect the occurrence of a transient in the ARMA model. We also apply the proposed method to detect transient changes in the pH of an erythromycin salt.     

基于自然元法和精细积分法的功能梯度材料瞬态热传导问题求解

为促进无网格法分析技术在热传导分析中的应用,提出空间离散采用自然单元法、时间离散采用精细积分法求解功能梯度材料瞬态热传导问题的数值计算方法.在计算过程中,取高斯点的材料参数模拟功能梯度材料特性的变化.温度场采用自然邻接点插值形函数进行离散插值.数值算例验证该数值算法的正确性和有效性.     

Optimization of nonlinear trusses using a displacement-based approach

A displacement-based optimization strategy is extended to the design of truss structures with geometric and material nonlinear responses. Unlike the traditional optimization approach that uses iterative finite element analyses to determine the structural response as the sizing variables are varied by the optimizer, the proposed method searches for an optimal solution by using the displacement degrees of freedom as design variables. Hence, the method is composed of two levels: an outer level problem where the optimal displacement field is searched using general nonlinear programming algorithms, and an inner problem where a set of optimal cross-sectional dimensions are computed for a given displacement field. For truss structures, the inner problem is a linear programming problem in terms of the sizing variables regardless of the nature of the governing equilibrium equations, which can be linear or nonlinear in displacements. The method has been applied to three test examples, which include material and geometric nonlinearities, for which it appears to be efficient and robust. Received December 4, 2000     

充液管道声压传感器设计

在分析管道导波机理的基础上,以管道中的流体为声压信号的传输介质,对充液刚性管道中的声场特点和声传播效应进行了研究,采用驻极体电容设计了能够检测充液管道中瞬变压力的声压传感器,透声材料封装使其兼有密封防水和声波透射双重功效,可实现主动防护监测和泄漏检测,在大港油田集油站现场实验取得了良好效果.     

Simultaneous optimization of the material properties and the topology of functionally graded structures

A level set based method is proposed for the simultaneous optimization of the material properties and the topology of functionally graded structures. The objective of the present study is to determine the optimal material properties (via the material volume fractions) and the structural topology to maximize the performance of the structure in a given application. In the proposed method, the volume fraction and the structural boundary are considered as the design variables, with the former being discretized as a scalar field and the latter being implicitly represented by the level set method. To perform simultaneous optimization, the two design variables are integrated into a common objective functional. Sensitivity analysis is conducted to obtain the descent directions. The optimization process is then expressed as the solution to a coupled Hamilton-Jacobi equation and diffusion partial differential equation. Numerical results are provided for the problem of mean compliance optimization in two dimensions.     

Continuum shape sensitivity analysis for aeroelastic gust using an arbitrary lagrangian-eulerian reference frame

Continuum Sensitivity Analysis (CSA), a method to determine response derivatives with respect to design variables, is derived here for the first time in an arbitrary Lagrangian-Eulerian (ALE) reference frame. CSA differentiates nonlinear governing system of equations to arrive at a linear system of partial differential continuum sensitivity equations (CSEs), here, for fluid-structure interaction (FSI). The CSEs and associated sensitivity boundary conditions are derived here for the first time for FSI, using the boundary velocity formulation, carefully distinguishing design velocity from flow velocity and ALE mesh velocity. Whereas boundary conditions must be differentiated using the material (total) derivative, it is sometimes advantageous to derive the CSEs using local (partial) derivatives. The benefit is that geometric sensitivity, known as design velocity, may not be required in the domain. It is shown here that this advantage is realized when the ALE frame undergoes only the rigid body motion associated with the structure to which it is attached. It is further shown that the advantage is not realized when the ALE mesh deforms due to the flexible motion of the fluid-structure interface. The equations for the transient gust response of a two-dimensional airfoil in compressible flow, flexibly attached to a rigid body mass, are presented as a model problem to illustrate a detailed derivation.     

一种模拟单粒子瞬态产生和测量方法

为了提高利用静态随机存取存储器(SRAM)型现场可编程门阵列(FPGA)评估集成电路单粒子瞬态(SET)的精度,在瞬态脉冲的产生方面以及瞬态脉冲在FPGA中的传播特性方面进行了研究。提出一种基于IDELAY2延迟元件的瞬态脉冲产生和测量方法,利用该方法可以连续产生和测量宽度增量为78ps的正脉冲(0-1-0)和负脉冲(1-0-1),同时在FPGA内部实现8种不同的门电路逻辑链,研究它们对瞬态脉冲宽度的影响。实验结果表明该瞬态脉冲产生和测量方法实现简单,可以在不改变电路布局布线的前提下,改变注入脉冲的宽度,且计算得到的理论脉冲宽度与实际测量的误差小于7%,同时8种不同的门电路逻辑链对瞬态脉冲宽度的影响和门类型以及脉冲类型有关,与初始输入瞬态脉冲宽度无关。     

用均场退火算法解四色问题

论文首先给出了用均场退火算法(AFA)求解四色问题的神经网络结构和能量函数,为了避免网络陷入局部极小的缺陷,在均场的基础上增加了“爬山”项,使网络最终能收敛到一个全局最优或近似全局最优解。仿真结果表明,该方法较文献[4]中的离散的二元Hopfield-型神经网络和文献[7]中的瞬态混沌神经网络在收敛速度方面有明显的提高,效果较好。     

Deflection of coupled elasticity–electrostatic bimorph PVDF material: theoretical,FEM and experimental verification

Piezoelectric materials have wide applications in the field of mechanical, aerospace and civil engineering because of its voltage dependent actuation. Piezoelectric material goes through voltage generation whenever deflection is induced in it and vice versa. Piezoelectric bimorph beam has been widely used for sensing and actuating. In the actuation mode, an electric field is applied across the beam thickness, one layer contracts while the other expands. This results in the bending of the entire structure and tip deflection. In the sensing mode, the bimorph is used to measure an external load by monitoring the piezoelectric induced electrode voltages. In this research work, a 2D bimorph piezoelectric actuator model having two layers made of polyvinylidene fluoride (PVDF) material was developed to examine the inverse piezoelectric effect. Finite element analysis (FEA) was carried out on specially designed actuator model by using MATLAB Partial Differential Equation (PDE) Toolbox™. Theoretical analysis has been carried out to measure the tip deflection under applied electric field. The laboratory test was performed to investigate the deformation behavior of piezoelectric actuator. It is observed that, more the electric field applied, more the material would be deformed in a particular direction. The experimental results are in good agreement with numerical results.

     

Electromagnetic signal processing An estimation/identification application

The response of an object subjected to high energy, transient electromagnetic fields sometimes called an electromagnetic pulse (EMP) is an important issue in the survivability of electronic systems (e.g. aircraft, computer systems, etc.), especially when the field has been generated by a high-altitude nuclear burst. The characterization of transient response information is a matter of national concern. In this paper, estimation and identification techniques are applied to: (1) improve signal processing at a test facility, and (2) parameterize a particular object response.First, the application of identification-based signal processing techniques to improve signal levels at the Lawrence Livermore National Laboratory (LLNL) Electromagnetic Test Facility is discussed. Models of test equipment are identified and then utilized in processing schemes to enhance or recover the desired signals. Parametric models of objects under test are identified from the enhanced data in order to extrapolate responses to threat levels.     

Finite element elastic-plastic-creep analysis of two-dimensional continuum with temperature dependent material properties

A technique is presented for performing finite element elastic-plastic-creep analysis of two-dimensional continuum composed of material with temperature dependent elastic, plastic, and creep properties. The plastic analysis utilizes the Prandtl-Reuss flow equations assuming isotropic material properties and linear strain-hardening. A power creep flow law formulated by Odquist is used to determine the steady state creep strain rate. The plastic and creep flow laws are employed to derive a ‘softened’ plastic-creep stress-strain matrix. These modified stress-strain relations are then used to formulate the element stiffness matrix in the usual manner. The differences in the elastic, plastic, and creep properties of the material due to the temperature change during the increment result in the formation of pseudo stresses, which in turn lead to load terms that appear on the right hand side of the equilibrium equations. The load terms resulting from these pseudo stresses not only keep the solution on the temperature dependent stress-strain curve of the material, but also correct for the elastic ‘overshoot’ that occurs when an element changes from an elastic to a plastic state. The effect of large displacements is included by the formulation of the geometric stiffness matrix for each element being used in the computer code. With this procedure it becomes economically feasible to perform elastic-plastic-creep stress analysis of two-dimensional continuum subjected to transient thermal and mechanical loadings. Several examples of both elastic-plastic and creep analyses are presented, and the finite element solutions are compared to either other theoretical solutions or experiment.     

高速燃油离心泵内流场分析和气蚀过程仿真

采用混合两相流模型和气蚀模型,采用两种网格技术多参考系模型和滑移网格模型对某型航空发动机高速燃油加力离心泵内流场和气蚀过程进行了二维数值仿真.首先使用多参考系模型得到稳态非气蚀流场,然后作为初始条件引入滑移网格技术同时加人气蚀模型对气蚀全过程进行了瞬态仿真.不仅良好地模拟出泵腔内空泡初生、发展、消失的瞬态全过程,同时发现了稳定的瞬态压力场和气泡体积分数场的周期性发展规律,并揭示这一规律由排出管引起.详细分析了气蚀易发生位置的空间分布,排出管对气蚀发生的影响,高度空化流中蜗室出口壁面处气蚀破坏及其成因.仿真结果与实物气蚀破坏情况符合良好,对认识高速离心泵内燃油流动,预测并克服气蚀发生有指导意义.     

Vibrations of an aramid anchor cable subjected to turbulent wind

The vibration response of an initially pre-stressed anchor cable made of parallel-lay aramid fibres excited by a measured and artificially simulated spatial turbulent wind field is presented in the paper. Results of the analyses of in situ measured wind records are described. For selected data set statistical characteristics and power spectral density functions of the measured wind velocity components are calculated. The wind stochastic velocity fluctuation is modelled as a one-variate bi-dimensional random field. Cross-power spectral density functions, at different point locations are introduced. The combination of the weighted amplitude wave superposition method (WAWS) with the Shinozuka–Deodatis method is used for the analyzed problem. A time-dependent behaviour of the synthetic cable is investigated which is subjected to turbulent wind with large expected oscillations that arise as a result of slackening due to the relaxation effects. A nonlinear transient dynamic analysis is used in conjunction with the finite element method to determine the dynamic response of the cable subjected to turbulent wind at its initially prestressed state and in the selected times after the relaxation effect. The constitutive equation of the relaxation of the aramid cable follows an experimentally obtained law of the logarithmic type. To monitor the dependences of the individual quantities of cable vibration in the phase space, attractors and Poincaré maps are created by sampling the cable’s displacement and velocity at periods of relevant frequencies. Interesting findings based on the response of the cable with rheological properties to turbulent wind are presented.